Physics · Ch 2 — Current Electricity
Ohm's Law
Ohm's Law
Starting directly from the microscopic form of Ohm's law, , consider a uniform segment of wire of length l and cross-sectional area A. Assuming the electric field is uniform along the wire's length, the potential difference (voltage) across it can be written , i.e. . Also, since , substituting both into gives (2.14), which rearranges to
The quantity depends only on the conductor's geometry (its length and area) and material (through ), and is defined as the resistance R of the conductor. This turns equation (2.15) into the everyday, macroscopic form of Ohm's law:
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What this figure shows. A straight cylindrical wire of length l and cross-sectional area A is shown with an electric field arrow E drawn along its axis, current I flowing through it, and the potential difference V marked across its two ends -- the exact geometric setup used to turn the microscopic relation into the macr …
What this figure shows. Two side-by-side I-versus-V graphs. Graph (a) shows a straight line passing through the origin, with its slope explicitly labelled as -- this is the signature of an ohmic material, whose resistance R stays constant regardless of the applied voltage. Graph (b) shows a curved, non-linear line (also starting near the origin) for a non-ohmic device such as a diode (covered later in Unit 9): because this curve's slope keeps changing, such a device has no single, consta …
Worked out. A potential difference of 12 V is applied across a resistor, and the current through it is required. Direct application of Ohm's law, A. This is the simplest possible one-step use of the macroscopic form of Ohm's law. …